In recent years the sport of water-skiing has become an increasingly popular form of water recreation. It is particularly enjoyable in large open expanses of water which permit high speed towing over long distances while performing manuevers which range over wide lateral areas. For example, in one such manuever an advanced water-skier will start on two skis, but then, when proper planing is obtained, the skier will drop or leave one ski behind and continue to be towed on one ski. Hence, large distances may be traveled away from the point where the one ski was left behind. Such large expanses and wide ranging manuevers do however create some drawbacks which, even at best, represent nuisances to water-skiing enthusiasts. For example, most open expanses of water are not usually flat calm. Consequently, detached skis are often difficult to see because even small wave actions tend to obscure a clear view of the water's surface. Moreover, since water-skis are generally designed with easy detachment from the skier as a paramount safety consideration, and since one common water-skiing manuever is to purposely step out of one water-ski and continue to ski on the remaining ski, a detached ski may come to rest a considerably distance from a downed skier. All this goes to say that at the speeds and distances involved in such manuevers and/or in the confusion of a fall, a detached water-ski is often difficult to locate, either from the nearby, but low-level vantage point of the skier in the water, or from the higher but usually farther distance of the towing boat. These difficulties are also exacerbated if a detached water-ski happens to come to rest upside down with its shoe piece facing down in the water. Under these circumstances the ski, which is typically less than an inch thick, takes on the character of a flat plank-like object and only a small fraction of an inch of its thickness will lie above the water's surface. In other words, an upside down, unattended water-ski is essentially submerged, and thus largely out of sight. This circumstance represents a far more serious problem than searching for a lost ski. Such an object, floating just at the water's surface, in an area trafficked by high-speed boats and skiers, represents a serious safety hazard.
In order to better understand some of the problems associated with locating water-skis in open water, and Applicant's particular approach to these problems, a little discussion of basic hydrostatics and hydrodynamics may be in order. We can begin this discussion by noting that the basic principle involved in hydrostatics is that of Archimedes: a floating object displaces its own weight in water. FIGS. 1(a), 1(b) and 1(c) are offered to further help explaining the hydrostatic principles employed in applicant's water-ski locator device. These three figures depict a vertical cross-section of a very generalized floating hull 10 in three hydrostatic states.
In all these figures, M represents the position of the center of mass of the entire assembly, out of the water. The force of gravity acts on the total assembly as if all of its mass were concentrated at this point, which, for a fixed rigid structure, remains in the same position relative to the assembly structure at all times. Point C represents the position of the center of buoyancy, the center of mass of water actually displaced by the immersed assembly at any time. This position is constantly moving as the structure lies at different attitudes as winds and waves cause it to roll and pitch in the water. Through Point C, there is focused, directly upwards, a force equal to the mass of the water displaced.
FIG. 1(a) shows a hull 10 laden with a cargo 11 in its bottom. In this state, the center of buoyancy C of the hull/cargo system lies above its center of mass M. For the sake of simplicity, both C and M are assumed to lie on the ship's vertical centerline 12--12'. When the center of buoyancy C and the center of mass M are so arranged with respect to each other, disturbances from a vertical orientation tend to raise the center of mass M relative to the center of buoyancy C. Such a disturbance causes the natural restorative forces present in this C above M state to bring the system back to its original condition. Thus, this is a hydrostatically stable situation. In other words, FIG. 1(a) is intended to show that a concentration of weight 11 in the lower portions of such a hull 10, symmetrical about center line 12--12', lowers the system's center of mass to a point M where a force, depicted by a downward pointing arrow, is assumed to be concentrated. Note that point M also lies well below the midpoint of the hull height H. The force directed downward from point M is opposed by a force, depicted by an arrow projecting upward from point C, which is provided by buoyancy. Again, this state, wherein point C lies above point M, is stable; consequently hull 10 floats in the erect orientation shown in FIG. 1(a) i.e., center line 12--12' is vertical.
FIG. 1(b) and 1(c) depict two possible changes to the stable hydrostatic arrangement of FIG. 1(a). FIG. 1(b) shows how a high cargo 14 placed on the deck of hull 10 will raise the center of mass M above the center of buoyancy C. This also forces the hull 10 deeper into the water and consequently lowers its center of buoyancy C. This condition is unstable: that is to say the forces exerted during any heeling action are offset from direct axial opposition, thus forming a rotational moment about this offset. This circumstance causes the list depicted in FIG. 1(b). In other words, in the high load situation depicted in FIG. 1(b), a force, at the center of mass M, is exerted downwardly at a point above the upward force exerted at the center of buoyancy C. This condition causes a "couple" depicted by the two curved arrow emanating from points M and C respectively. Again, this condition is unstable; hence the hull 10 tends to capsize as indicated.
FIG. 1(c) shows the case where the hull 10 is so light (load 11 is removed) that, overall, it floats with its center of mass M above its center of buoyancy C as well as above water line 16. Here again, because point M is above point C, a couple is created and the hull 10 tends to capsize. As will be pointed out in greater detail, Applicant's water-ski locator device is deliberately designed to create this particular hydrostatically unstable situation if the detached ski happens to come to rest upside down i.e., with the ski's shoe piece facing downward in the water. However, before more fully discussing this aspect of Applicant's water-ski locator device, it also would be helpful to note how the prior art addressed the problems associated with free floating water-skis.
Various devices for changing the hydrostatics of floating water-skis have been proposed in order to make them more visible. Generally they involve the use of a variety of floats, buoyancy-providing core materials and water-ski locator attachments. Of these devices, three patent references might well be cited as being the most representative of the prior art methods of making detached water-skis more visible in the water. For example, U.S. Pat. No. 3,031,697, teaches the use of an especially buoyant ski tip used in conjunction with a weight added to the stern end of the water-ski. This arrangement causes the bow tip of the ski to project from the water when the ski is floating free in the water. U.S. Pat. No. 3,066,326 also discloses the use of an especially buoyant ski tip cover which can be detachably mounted t the bow end of the ski. U.S. Pat. No. 3,212,113, proposes use of a ball-like float which is attached to a rope tethered to the top side of the stern end of a water-ski.
All of these prior art water-ski locator devices, however, have at least one common drawback which applicant's invention seeks to overcome. To some degree, each of these prior art devices remains in drag-creating contact with the water during skiing operations. Such drag is usually regarded as undesirable by most water-skiers. Moreover, some of these prior art water-ski locator devices also change the normal contour of the ski itself. Hence, water-skis equipped with such drag creating and/or contour-changing locator devices do not "feel" the same to the water-skier as they would without them.
A beginning appreciation of applicant's solution to the drag problem created by such prior art water-ski locator devices can be gained by first considering the hydrodynamics of a ski traveling through the water. This action is described by Bernouilli's Principle even though it does not act in the same way as the lift provided to an airplane wing due to motion through a homogenous fluid/air. In the case of a moving hull such as a water-ski under strong towing action, there is movement along the interface of two fluids (air and water) having markedly different densities. Here the relevant forces combine to produce the phenomenon known as "planing".
FIGS. 2 and 3 respectively portray a plan and a side view of the normal disturbance of tee water's surface during water-skiing. Under the action of a pulling force 13, the ski 19 is pulled through the water 16, and the ski's velocity is converted into hydrostatic head depicted as arrows 23 along the flat underside of the ski below the waterline. This pulling action causes the ski to throw a bow wave 20 which propagates outwardly directly from the ski-water interface generally in the area slightly forward from ski's toe piece 22. Water is thrown straight outward from the ski's bottom side until, somewhere in the region behind the skier's foot, an after portion 24 of the ski is in the water deep enough to permit a supersurface wave 26 to roll in toward the stern. FIG. 3 is, among other things, specifically intended to show that no drag creating contact with the water is made near a front cuff region 27 as the ski 19 advances under the towing or pulling action 18 provided by a boat, not shown. This wave behavior and lack of water contact in the front cuff region 27 can be verified by observing that expert skiers, as a "trick", are able to quick-start, fully dressed, from a dry beach, ski in water and then return to the beach without soaking their trouser cuffs.
Therefore, Applicant has concluded that since any unnecessary drag and/or changes in the water-ski's contour will be, to some degree, detrimental to smooth water-skiing actions and since the "front trouser cuff region" 27 is not in contact with the water during water-skiing operations, this would be a particularly advantageous place for placement of a water-ski locating device because when located here, it would not create drag or otherwise interfere with the water-ski's normal hydrodynamics. Moreover, the positioning of a buoyant water-ski locator device in this front trouser cuff region 27 will also better serve to "roll over" a water-ski if it comes to rest upside down ala the coupling principles depicted in FIG. 1(c). Such a rolling over, for reasons which are hereinafter more fully described, will make the locator device, and hence the ski itself, much more visible in the water.